Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;

int N;
int Data[1000];
multiset<int> Numbers;

int main() {
	double maxSum, minSub, ans;

	Numbers.clear();
	cin >> N;
	for (int i = 0; i < N; ++i) {
		cin >> Data[i];
		Numbers.insert(Data[i]);
	}

	ans = 0.0;
	for (int i = 0; i < N; ++i) {
		Numbers.erase(Numbers.find(Data[i]));
		for (int j = 0; j < N; ++j) {
			if (i == j) {
				continue;
			}
			Numbers.erase(Numbers.find(Data[j]));
			maxSum = *(Numbers.rbegin()) + *(++Numbers.rbegin());
			minSub = abs(Data[i] - Data[j]);
			ans = max(ans, maxSum / minSub);
			Numbers.insert(Data[j]);
		}
		Numbers.insert(Data[i]);
	}
	cout << fixed << setprecision(6) << ans << endl;

	return 0;
}